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Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case

Abstract : We consider a closed three-dimensional contact sub-Riemannian manifold. The objective of this note is to provide a precise description of the sub-Riemannian geodesics with large initial momenta: we prove that they "spiral around the Reeb orbits", not only in the phase space but also in the configuration space. Our analysis is based on a normal form along any Reeb orbit due to Melrose.
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https://hal.archives-ouvertes.fr/hal-03151365
Contributor : Emmanuel Trélat <>
Submitted on : Wednesday, February 24, 2021 - 4:45:53 PM
Last modification on : Tuesday, March 16, 2021 - 9:57:13 AM

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  • HAL Id : hal-03151365, version 1

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Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat. Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case. 2021. ⟨hal-03151365⟩

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